Escapement for a timepiece with optimized torque transmission

Abstract

An escapement for a timepiece, comprising: —an escapement wheel pivotally mounted around a corresponding axis of rotation and intended to be driven by a drive source, said escapement wheel comprising a plurality of teeth; —a pallet fork pivotably mounted around a corresponding axis of rotation, said pallet fork comprising an entry pallet and an exit pallet, each pallet comprising a rest face arranged to block the escapement wheel, as well as a pulse face arranged to interact with the escapement wheel in order to transmit the pulses received from the latter to a regulating member arranged to perform oscillations, said pallet fork being arranged to free the escapement wheel periodically under the control of the regulating member, characterized in that at least one of the pulse faces is shaped in such a way that, on at least one portion of the pulse face, and considered at each point of contact (C′) between the escapement wheel and the pulse face, the tangent of the pulse face intersects the center-to-center distance between the escapement wheel and the pallet fork according to an angle (αorientation) that observes a particular relation.

Claims

1. An escapement for a timepiece, comprising: an escapement wheel mounted in a pivotable manner about a corresponding axis of rotation and intended to be driven by a power source, said escapement wheel including a plurality of teeth; an anchor mounted in a pivotable manner about a corresponding axis of rotation, said anchor comprising an entry pallet and an exit pallet, each pallet comprising a rest surface arranged to block said escapement wheel, as well as an impulsion surface arranged to interact with said escapement wheel in order to transmit impulsions received from the latter to a regulating member arranged to produce oscillations, said anchor being arranged to release said escapement wheel periodically under the control of said regulating member, wherein at least one of said impulsion surfaces is configured in such a way that, on at least one part of said impulsion surface, and considered at each point of contact between the escapement wheel and said impulsion surface, the tangent of said impulsion surface intersects a center-to-center line between the escapement wheel and the anchor at an angle α.sub.orientation which observes the relationship: ${\alpha }_{\mathrm{orientation}}=\alpha -\mathrm{COF}+{\tan }^{-1}\left(\frac{C*R+\cos \left(\alpha -\theta \right)*R_2}{R_2*\sin \left(\alpha -\theta \right)}\right)\text{+/–}10\%$ where
R.sub.2=√{square root over (R.sup.2*sin.sup.2(α)+(−R*cos(α)+L).sup.2)} and where $\theta ={\tan }^{-1}\left(R*\frac{\sin \left(\alpha \right)}{L-R*\cos \left(\alpha \right)}\right)$ in which all the angles are expressed in radians, and α.sub.orientation &is the angle between said tangent with said center-to-center line; α is the angle between a line joining said point of contact and the axis of rotation of said escapement wheel and said center-to-center line; COF is the trigonometric tangent of the coefficient of friction between the escapement wheel and said impulsion surface; R is the distance between the axis of rotation of said escapement wheel and said point of contact, +/−10%; C is the torque ratio between that of the anchor and that of the escapement wheel; L is the length of said center-to-center line.

2. The escapement as claimed in claim 1, in which the impulsion surface of the entry pallet is convex.

3. The escapement as claimed in claim 1, in which the impulsion surface of the exit pallet is concave.

4. The escapement as claimed claim 1, in which the escapement wheel includes teeth having convex impulsion surfaces.

5. An escapement for a timepiece, comprising: an escapement wheel mounted in a pivotable manner about a corresponding axis of rotation and intended to be driven by a power source, said escapement wheel including a plurality of teeth; an anchor mounted in a pivotable manner about a corresponding axis of rotation, said anchor comprising an entry pallet and an exit pallet, each pallet comprising a rest surface arranged to block said escapement wheel, as well as an impulsion surface arranged to interact with said escapement wheel in order to transmit impulsions received from the latter to a regulating member arranged to produce oscillations, said anchor being arranged to release said escapement wheel periodically under the control of said regulating member, wherein, on at least one part of an impulsion surface that each of said teeth includes, and considered at each point of contact between said impulsion surface and one of said pallets, the tangent of said impulsion surface intersects a center-to-center line between the escapement wheel and the anchor at an angle α.sub.orientation which observes the relationship ${\alpha }_{\mathrm{orientation}}={\tan }^{-1}\left(\frac{R*\mathrm{Seuil}*\alpha *\cos \left(\alpha \right)+C*R*\cos \left(\alpha \right)+R*\cos \left(\alpha \right)-L}{R*\sin \left(\alpha \right)*\left(\mathrm{Seuil}*\alpha +C-1\right)}\right)\text{+/–}10\%$ in which α.sub.orientation is the angle between said tangent and said center-to-center line; α is the angle between a line joining said point of contact and the axis of rotation of said escapement wheel and said center-to-center line; Seuil is value for a lifting-off threshold between the escapement wheel and the anchor; R is the distance between the axis of rotation of said escapement wheel and said point of contact, +/−10%; C is the torque ratio between that of the anchor and that of the escapement wheel; L is the length of said center-to-center line.

6. The escapement as claimed in claim 5, in which the escapement wheel includes teeth having convex impulsion surfaces.

7. The escapement as claimed in claim 5, in which said value Seuil is a function of the first derivative of the speed ratio of the anchor on the escapement wheel at the time of the impulsion on the beak of said pallet.

8. An escapement for a timepiece, comprising: an escapement wheel mounted in a pivotable manner about a corresponding axis of rotation and intended to be driven by a power source, said escapement wheel including a plurality of teeth; an anchor mounted in a pivotable manner about a corresponding axis of rotation, said anchor comprising an entry pallet and an exit pallet, each pallet comprising a rest surface arranged to block said escapement wheel, as well as an impulsion surface arranged to interact with said escapement wheel in order to transmit impulsions received from the latter to a regulating member arranged to produce oscillations, said anchor being arranged to release said escapement wheel periodically under the control of said regulating member, wherein at least one of said impulsion surfaces is configured in such a way that, on at least one part of said impulsion surface, and considered at each point of contact between the escapement wheel and said impulsion surface, the tangent of said impulsion surface intersects a center-to-center line between the escapement wheel and the anchor at an angle α.sub.orientation which observes the relationship: ${\alpha }_{\mathrm{orientation}}=\alpha -\mathrm{COF}+{\tan }^{-1}\left(\frac{C*R+\cos \left(\alpha -\theta \right)*R_2}{R_2*\sin \left(\alpha -\theta \right)}\right)\text{+/–}10\%$ where
R.sub.2=√{square root over (R.sup.2*sin.sup.2(α)+(−R*cos(α)+L).sup.2)} and where $\theta ={\tan }^{-1}\left(R*\frac{\sin \left(\alpha \right)}{L-R*\cos \left(\alpha \right)}\right)$ in which all the angles are expressed in radians, and α.sub.orientation is the angle between said tangent with said center-to-center line; α is the angle between a line joining said point of contact and the axis of rotation of said escapement wheel and said center-to-center line; COF is the trigonometric tangent of the coefficient of friction between the escapement wheel and said impulsion surface; R is the distance between the axis of rotation of said escapement wheel and said point of contact, +/−10%; C is the torque ratio between that of the anchor and that of the escapement wheel; L is the length of said center-to-center line; and wherein, on at least one part of an impulsion surface that each of said teeth includes, and considered at each point of contact between said impulsion surface and one of said pallets, the tangent of said impulsion surface intersects a center-to-center line between the escapement wheel and the anchor at an angle α.sub.orientation which observes the relationship ${\alpha }_{\mathrm{orientation}}={\tan }^{-1}\left(\frac{R*\mathrm{Seuil}*\alpha *\cos \left(\alpha \right)+C*R*\cos \left(\alpha \right)+R*\cos \left(\alpha \right)-L}{R*\sin \left(\alpha \right)*\left(\mathrm{Seuil}*\alpha +C-1\right)}\right)\text{+/–}10\%$ in which α.sub.orientation is the angle between said tangent and said center-to-center line; α is the angle between a line joining said point of contact and the axis of rotation of said escapement wheel and said center-to-center line; Seuil is value for a lifting-off threshold between the escapement wheel and the anchor; R is the distance between the axis of rotation of said escapement wheel and said point of contact, +/−10%; C is the torque ratio between that of the anchor and that of the escapement wheel; L is the length of said center-to-center line.

9. A watch movement comprising an escapement as claimed in claim 1.

10. A timepiece comprising a movement according to claim 9.

11. A watch movement comprising an escapement as claimed in claim 5.

12. A timepiece comprising a movement according to claim 10.

13. A watch movement comprising an escapement as claimed in claim 8.

14. A timepiece comprising a movement according to claim 13.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be more readily appreciated by reading the following description of an embodiment, given by way of example and made with reference to the drawings, in which:

(2) FIG. 1 represents a schematic plan view of an escapement according to the invention;

(3) FIG. 2 represents an enlarged view of a tooth of the escapement wheel and of the entry pallet;

(4) FIG. 3 represents an enlarged view of the exit pallet;

(5) FIG. 4 represents a schematic modeling of the point of contact between the anchor and the escapement wheel;

(6) FIG. 5 represents an exaggerated schematic view of the development of the tangent of the profile of the impulsion surface of the entry pallet during the impulsion phase;

(7) FIG. 6 represents an exaggerated schematic view of the development of the tangent of the profile of the impulsion surface of the exit pallet during the impulsion phase;

(8) FIG. 7 represents a graph of the development of the tangent of the profile of the impulsion surface of the entry pallet during the impulsion phase, in terms of the angle and in terms of time;

(9) FIG. 8 represents a graph of the development of the tangent of the profile of the impulsion surface of the exit pallet during the impulsion phase, in terms of the angle and in terms of time;

(10) FIG. 9 represents an exaggerated schematic view of the development of the tangent of the profile of the impulsion surface of a tooth of the escapement wheel during the impulsion phase;

(11) FIG. 10 represents a graph of the development of the tangent of the profile of the impulsion surface of a tooth of the escapement wheel during the impulsion phase; and

(12) FIG. 11 represent a graph of the development of the speed ratio of the anchor on the escapement wheel in the course of the impulsion phase.

EMBODIMENTS OF THE INVENTION

(13) FIG. 1 depicts an escapement 1 according to the invention. This escapement 1 embodies the overall form of a Swiss anchor escapement, in which each pallet participates in providing an impulsion to the regulating member.

(14) As generally known, the escapement comprises an escapement wheel 3, arranged to be driven by a power source, not depicted here. This power source may be a mainspring or an electric motor, for example, which is kinematically linked with the escapement wheel 3 by means of a going train (likewise not depicted).

(15) The escapement wheel 3 is mounted in a pivotable manner on an arbor (not depicted), of which the theoretical axis is indicated by the reference sign 5. In the variant depicted here, the teeth of the escapement wheel 7 each include an upstream surface 7a, which interacts with the pallets when the escapement wheel 3 is blocked, and an impulsion surface. However, the invention is applicable to other forms of escapement wheel, for example to pointed teeth (English anchor escapement), or to less conventional forms.

(16) The teeth 7 of the escapement wheel 3 interact in a known manner with an anchor 9, which pivots about a theoretical axis of rotation 11. In the variant depicted here, this theoretical axis 11 coincides with an arbor (not depicted), but an anchor of the “suspended” type as described in document CH708113, or of any other appropriate type, is equally possible. The line joining the axis of rotation 5 of the escapement wheel 3 and that of the anchor defines a center-to-center line 12.

(17) The overall form of the depicted anchor 9 is traditional. In this respect, it includes a rod 9a extending from the axis of rotation 11 and terminating in a fork 9c, which interacts with a regulating member (not depicted) in a known manner in order to cause it to oscillate with a predetermined periodicity, which need not be described here in detail. Furthermore, a pair of arms 9b extend to either side of the axis of rotation 11 in directions substantially perpendicular to the rod 9a, and are terminated by pallets 13, 15. It goes without saying that other less common forms of anchor may also be utilized within the framework of the invention.

(18) Each of these pallets 13, 15 is arranged to block and to release the escapement wheel periodically, the latter being blocked by one of the pallets 13, 15 and then re-blocked by the other, in sequence.

(19) The pallet 13 depicted on the right in FIG. 1 is the entry pallet, situated upstream in the direction of rotation of the escapement wheel 3 indicated by the arrow, and the pallet 15, situated downstream, is the exit pallet.

(20) In the variant depicted here, the pallets 13, 15 are integral with the anchor 9, although the invention is likewise applicable to pallets attached to the arms 9b. Each pallet 13, 15 includes, as generally known, a rest surface 13a, 15a respectively, and an impulsion surface 13b, 15b respectively. The rest surfaces 13a, 15a, serve to block the escapement wheel 3 during rest phases, and the impulsion surfaces 13b, 15b cooperate with the teeth 7 in order to transmit an impulsion to the anchor and thus to the regulating member during the impulsion phase. Each of these teeth 7 includes a rest beak 7c, which interacts with the rest surfaces 13a, 15a of the pallets 13, 15, as well as an oblique impulsion surface 7b. The rest beak 7c, which is present between the upstream surface 7a and the impulsion surface 7b, as well as this impulsion surface 7b, contribute to transmit an impulsion to the anchor 9.

(21) In a typical escapement of the kind that has just been defined, the rest surfaces 13a, 15a are typically planes, of which the angle is selected in such a way that, during rest phases, the force F resulting from contact between the rest surface 13a, 15a and the tooth 7 comprises a component which tends to keep the pallet 13 or 15, as appropriate, engaged with the escapement wheel 3. This force F as a result generates a torque about the axis of rotation 11 of the anchor 9, which tends to cause the anchor to pivot in the anticlockwise direction (according to the orientation in FIG. 1) when the entry pallet 13 is engaged, and in the clockwise direction when the exit pallet 15 is engaged.

(22) In a typical escapement, the impulsion surfaces of the pallets 13b, 15b are typically planes, which, during the impulsions, causes a reduction in the torque transmitted from the escapement wheel 3 to the anchor 9 during each impulsion phase. This variation in torque is inefficient and limits the performance of the escapement 1.

(23) The invention, as a result, primarily concerns the form of the impulsion surfaces 13b, 15b of the pallets 13, 15, as well as that of the impulsion surface 7b of the teeth 7 of the escapement wheel 3. Since the active surfaces 13a, 13b, 15a, 15b of the pallets are not, or at least do not need to be, planar, the terminology of “surface” is utilized in place of the usual formulation “plane of . . . ”.

(24) FIG. 4 depicts a modeling schematic which may be utilized for calculating the form of the impulsion surfaces of the pallets. The geometrical relationship between the point of contact C′ between the impulsion surface 13b of the entry pallet and a tooth 7 of the escapement wheel 3, the escapement wheel 3 and the center-to-center line 12 is depicted in the diagram which constitutes this figure.

(25) In order for the force F that the escapement wheel 3 exerts on the entry pallet 13 to generate a torque which is constant throughout the impulsion phase, the angle α.sub.orientation between the tangent of the impulsion surface 13b of the entry pallet and the center-to-center line 12 must observe the following relationship, obtained by resolving the forces, at each point during the impulsion phase:

(26) ${\alpha }_{\mathrm{orientation}}=\alpha -\mathrm{COF}+{\tan }^{-1}\left(\frac{C*R+\cos \left(\alpha -\theta \right)*R_2}{R_2*\sin \left(\alpha -\theta \right)}\right)$
where
R.sub.2=√{square root over (R.sup.2*sin.sup.2(α)+(−R*cos(α)+L).sup.2)}
and where

(27) $\theta ={\tan }^{-1}\left(R*\frac{\sin \left(\alpha \right)}{L-R*\cos \left(\alpha \right)}\right)$

(28) A tolerance of +/−10%, preferably +/−7%, more preferably +/−5% or even +/−3% or +/−2% can be added to the relationship which defines α.sub.orientation, in order for it to exhibit realistic manufacturing tolerances.

(29) In these equations, all the angles are expressed in radians. α is the angle between a line joining said point of contact and the axis of rotation of said escapement wheel 3, and said center-to-center line 12, defined mathematically. This angle decreases, therefore, during the impulsion phase on the entry pallet 13, since the point of contact C′ moves closer to the center-to-center line 12 when the escapement wheel 3 rotates. COF is the trigonometric tangent (in radians) of the coefficient of friction between the escapement wheel and said impulsion surface, that is to say tan(μ) according to the conventional notation; R is the distance between the axis of rotation of said escapement wheel and said point of contact, with a tolerance of +/−10%, preferably +/−7%, more preferably +/−5% or even +/−3% or +/−2%, in order for it to exhibit realistic manufacturing tolerances; C is the torque ratio between that of the anchor in relation to that of the escapement wheel, that is to say C.sub.anchor/C.sub.wheel; and L is the length of said center-to-center line 12.

(30) It should be noted that, in view of the tolerance on the value of R as well as that on α.sub.orientation, the invention encompasses a family of possible curves. This is inevitable in view of the manufacturing tolerances, since it is very difficult to manufacture, in a reproducible manner, a curve which is mathematically perfect.

(31) The same relationship is equally valid for the exit pallet 15, since the geometry is similar, the point of contact C′ being situated, of course, on the other side of the center-to-center line 12.

(32) FIG. 5 depicts, in an exaggerated manner, the development of α.sub.orientation of the impulsion surface 13b of the entry pallet 13 during its impulsion phase. It is clear that, when the escapement wheel 3 turns and the point of contact C′ advances on an arc of a circle, the angle α.sub.orientation increases when α decreases for the raisons explained above. FIG. 7 depicts this increase as a function of the angle α(t) of the point of contact C′ in the course of time, and the values of the angle α.sub.orientation thereby calculated at a plurality of points may be utilized to define tangents which may be combined in a smooth manner in order to define the form of the impulsion surface 13b of the entry pallet 13, for at least one part of its length. This part may extend, for example, for at least 20%, at least 40%, at least 50%, at least 60% or even at least 80% or 90% of the length of said impulsion surface 13b. According to these figures, it is clear that said impulsion surface 13 will be convex.

(33) Similarly, FIG. 6 depicts, likewise in an exaggerated manner, the development of α.sub.orientation of the impulsion surface 15b of the exit pallet 15 throughout its impulsion phase. It is clear, when the escapement wheel 3 turns and the point of contact C′ advances on an arc of a circle, that the angle α.sub.orientation decreases. FIG. 8 depicts this decrease as a function of the angle α of the point of contact C′; in fact, in the course of the movement, α moves away from the center-to-center line or α is strictly negative in the trigonometric sense, and therefore α(t) decreases in the course of the movement. Once again, the angles α.sub.orientation thereby calculated may be utilized in order to define tangents which may be combined in order to define the form of the impulsion surface 15b of the exit pallet 15, for at least one part of its length. This part may extend, for example, for at least 20%, at least 40%, at least 50%, at least 60% or even at least 80% or 90% of the length of said impulsion surface 15b. In the case of the exit pallet 15, the angle α increases during the corresponding impulsion phase, since the point of contact C′ moves away from the center-to-center line 12. According to these figures, it is clear that said impulsion surface 15 will be concave.

(34) In the light of the foregoing, the forms of the impulsion planes 13b, 15b of the pallets may be determined for an escapement exhibiting a given geometry, also taking account of the form of the impulsion surfaces 7b of the teeth 7 of the escapement wheel 3, which determines the development of the position of the point of contact with the pallets 13, 15 during the impulsion phases.

(35) Even if the forms of the pallets 13, 15 as determined above may be utilized in conjunction with an escapement wheel of known form, it is advantageous to adapt the form of the impulsion surfaces 7b in such a way that lifting-off of the pallet from the escapement wheel is avoided.

(36) In essence, in the case of a conventional escapement, when the tooth 7 of the escapement wheel 3 performs the transition from the rest surface 13a, 15a of a pallet to its impulsion surface 13b, 15b (known as “impulsion on the pallet”, since the tooth 7 interacts with the impulsion surface 13b, 15b of the pallet), an acceleration of the escapement wheel 3 and of the anchor 9 takes place. Furthermore, during the latter part of the impulsion phase, when the tooth interacts with the downstream beak 13c, 15c of the pallet 13, 15 (known as “impulsion on the tooth”, since it is the downstream beak 13c, 15c of the pallet which interacts with the tooth 7), a second, even stronger acceleration is created. If these accelerations are too great, the pallet 13, 15 may separate from the escapement wheel 3, the effect of which is for the contact between these two elements to be interrupted.

(37) The profile of the impulsion surface 7b of the teeth 7 of the escapement wheel can be determined, starting from the same model depicted in FIG. 4, which prevents such a lifting-off during the transition from the impulsion surface 7b to the downstream beak 7d.

(38) According to the geometry of the contact between the escapement wheel 3 and the impulsion surface 13b, 15b of the one of the pallets, a torque ratio C between the torque of the anchor and the torque of the escapement wheel can be calculated as a function of the angle α as follows:

(39) $C\left(\alpha \right)=-\frac{R_2}{R}*\frac{\cos \left({\alpha }_{\mathrm{orientation}}-\theta +\mathrm{COF}\right)}{\cos \left({\alpha }_{\mathrm{orientation}}-\alpha +\mathrm{COF}\right)}$

(40) In this case, α.sub.orientation represents the angle formed between the tangent of the impulsion surface 7b of the tooth 7 at the point of contact C′ and the center-to-center line 12, the other variables being as described above. In the context of the profile of the impulsion surfaces 13b, 15b of the pallets 13, 15. In order to prevent lifting-off, the value C must be smaller than a predefined threshold value (see below).

(41) During the impulsion phase on the tooth, that is to say when the downstream beak 13c, 15c is in contact with the impulsion surface 7b of a tooth 7 of the escapement wheel 3,
C(α)≤Seuil*α+C
where C is the torque ratio at this change of beak and Seuil is a value of a lifting-off threshold calculated by experimentation or by modeling, or even defined arbitrarily. In more practical terms, a threshold derivative of the speed ratio of the anchor 9 on the wheel 3 can be defined, for example, by modeling. The parameter Seuil is influenced to such an extent by the geometry of the escapement, although modelizations have indicated that a value not exceeding 0.01, preferably not exceeding 0.005, are generally applicable, or at any rate may serve as points of departure.

(42) Consequently,

(43) $\mathrm{Seuil}*\alpha +C=-\frac{R_2}{R}*\frac{\cos \left({\alpha }_{\mathrm{orientation}}-\theta +\mathrm{COF}\right)}{\cos \left({\alpha }_{\mathrm{orientation}}-\alpha +\mathrm{COF}\right)}\mathrm{and}{\alpha }_{\mathrm{orientation}}={\tan }^{-1}\left(\frac{R*\mathrm{Seuil}*\alpha *\cos \left(\alpha \right)+C*R*\cos \left(\alpha \right)+R*\cos \left(\alpha \right)-L}{R*\sin \left(\alpha \right)*\left(\mathrm{Seuil}*\alpha +C-1\right)}\right)$

(44) In this relationship, a tolerance of +/−10%, preferably +/−7%, more preferably +/−5% or even +/−3% or +/−2% can be added to the value of α.sub.orientation, in order to exhibit realistic manufacturing tolerances. It should be noted that, in view of the tolerance on the value of R as well as that on α.sub.orientation, the invention encompasses a family of possible curves. This is inevitable in view of the manufacturing tolerances, since it is very difficult to manufacture, in a reproducible manner, a curve that is mathematically perfect.

(45) As a result, when α increases during the impulsion phase, α.sub.orientation increases likewise, in an approximately linear fashion. Thus, the profile of the impulsion surface 7b of the teeth 7 is convex, as depicted in exaggerated form in FIG. 9. The development of α.sub.orientation as a function of the angle α is likewise depicted in FIG. 10.

(46) Once again, as is the case for the pallets 13, 15, the angle α.sub.orientation may be calculated at several points, in order to determine the profile of said impulsion surface 7b in the manner referred to above.

(47) FIG. 11 is a normalized graph illustrating a comparison of the speed ratio of the anchor 9 on the escapement wheel 3 on an unlocking and an impulsion, for a conventional escapement (“Rv standard profiles”) and an escapement according to the invention (“Rv curved profiles”). This graph depicts both the effect of the form of the impulsion surfaces 13b, 15b, which assures a transmission of constant torque during the impulsion phase on the impulsion surface 7b of a tooth 7, and the effect of the curved profile of the teeth 7 of the escapement wheel.

(48) As far as concerns the transmission of constant torque, looking at the part of the graph indicated by “impulsion on the pallet”, for the conventional escapement, the speed ratio “Rv standard profiles” decreases throughout this phase, for the reasons mentioned above. On the other hand, for the escapement according to the invention, the speed ratio “Rv curved profiles” remains constant, since the torque ratio remains constant. It is likewise clear from this graph that the integral of the function “Rv curved profiles” during the impulsion phase on the surface is greater than that of “Rv standard profiles”, and that consequently more energy is supplied to the anchor during this phase of the impulsion. In fact, the above-mentioned value Seuil may be determined by considering the desired incline for the line “Rv curved profiles” during the impulsion on the tooth, which represents the first derivative of the angular speed ratio.

(49) This graph also illustrates the effect of the curved profile of the impulsion surface 7b of the teeth 7 of the escapement wheel 3. Since this surface 7b is curved, the incline of the curve of the speed ratio presents a significantly smaller incline than that which is present in the conventional case “Rv standard profiles”. A lifting-off may thus be avoided.

(50) In the case in which the form of the impulsion planes 7b of the teeth 7 of the escapement wheel 3 is straight, the corresponding curve will follow that of the “Rv curved profiles” until the intersection with the vertical line has the normalized value 800, and will then be combined with that of the “Rv standard profiles” until the end of the impulsion phase.

(51) Although this profile of the impulsion surfaces 7b of the teeth 7 of the escapement wheel 3 is depicted here in combination with the optimized forms of the pallets 13, 15, it may nevertheless be utilized with known pallets, for example pallets exhibiting standard planes.

(52) Calculations have shown that the form of the impulsion surfaces 13b, 15b of the pallets 13, 15 increases the performance by about 2 to 3 points, and the form of the impulsion surface 7b of the teeth 7 of the escapement wheel increases it by about 2 to 3 points extra. The combination of the two optimizations consequently adds about 4 to 6 performance points to the escapement.

(53) The anchor 9 and/or the escapement wheel 3 described above may, for example, be manufactured by micro-machining processes, such as LIGA, 3D printing, masking and engraving from a sheet of material, by stereolithography or similar. Appropriate materials may be selected, for example, from among the monocrystalline, polycrystalline or amorphous metals (such as steel, nickel-phosphorus, brass and similar), the non-metals such as silicon, its oxide, its nitride or its carbide, alumina in all its forms, diamond (including adamantine carbon), these non-metallic materials being monocrystalline or polycrystalline. All these materials may possibly be coated with another hard and/or anti-friction material, such as adamantine carbon or silicon oxide.

(54) The utilization of these curved profiles brings about an improvement in the performance of the escapement 1 in the order of 5% if the profiles are adopted on the pallets 13, 15 and on the escapement wheel 3.

(55) Although the invention is described above in conjunction with specific embodiments, additional variants are also conceivable without departing from the scope of the invention as defined by the claims.